How many palindromes below 10000 (i.e. between 0 and 9999 inclusively) are not divisible by 11?

List them.

A number is divisible by 11 if and only if the sum of its odd-numbered digits (1st digit, 3rd digit, 5th digit, etc.) minus the sum of its odd-numbered digits are divisible by 11. Thus, all palindromes with an even number of digits are divisible by 11. Thus, we must only consider palindromes with an odd number of digits.

All 10 one-digit numbers ( 0, 1, ... 8, 9) qualify.

Also, all 90 of the 3 digit palindromes except:

121

242

363

484

616

737

858

979

In other words, 10 + 90 - 8 = 92. Too many for me to list.